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A304447 Coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(2*n). 2
1, 4, 40, 448, 5264, 63624, 783328, 9770240, 123040288, 1561033348, 19922193200, 255472920256, 3289122824000, 42488488508808, 550435283089088, 7148519205631488, 93038785849116736, 1213215382135324680, 15846906866928513736, 207302985358274247104 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..880

FORMULA

a(n) ~ c * d^n / sqrt(n), where d = 13.43567525239504624062504283058713960962824709850658926621911428148173077464... and c = 0.3323527904383991069791889982282236666403568774227549868882810268779...

MATHEMATICA

nmax = 20; Table[SeriesCoefficient[Product[((1+x^k)/(1-x^k))^(2*n), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

nmax = 20; Table[SeriesCoefficient[(QPochhammer[-1, x]/2/QPochhammer[x])^(2*n), {x, 0, n}], {n, 0, nmax}]

CROSSREFS

Cf. A261386, A270919, A304443, A304444, A304448.

Sequence in context: A221588 A114468 A264112 * A002705 A235372 A034385

Adjacent sequences:  A304444 A304445 A304446 * A304448 A304449 A304450

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 12 2018

STATUS

approved

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Last modified September 17 08:31 EDT 2019. Contains 327127 sequences. (Running on oeis4.)